Metamaterials (MMs) are artificial composite materials and can
exhibit special electromagnetic (EM) properties which do not exist in
natural materials [1-3]. Based on the MMs, arbitrary values of effective
permittivity and permeability can be designed, so one can design some
amazing function device such as perfect lens [4] and invisible cloaking
[5]. In recent years, the research in chiral metamaterials (CMMs) has
been growing rapidly due to their special electromagnetic properties
which are optical activity and circular dichroism [6-12]. On the
strength of these peculiarities, CMMs have been proposed to manipulate
polarization states of electromagnetic waves for achieving polarization
rotation [13-29]. For example, a CMM pattern composed of twisted four
U-shaped split ring resonators with negative refractive index has been
proposed [28], which transforms incident linearly polarized waves into
circularly polarized waves with different directions of rotation at two
distinct resonances. However, as a circular polarizer, it has relatively
low polarization extinction ratio and polarization conversion
efficiency. Recently, Cheng et al. [15] studied a double-layered split
ring resonator structure to get a LCP and RCP wave with relatively high
polarization conversion efficiency, but only single-band LCP and RCP
wave can be obtained by this CMM. In order to increase the resonant
frequency, multi-band circular polarizer by using multi-layered planar
spiral array has been reported [17, 21]. In addition, other chiral
structures have been reported, such as cross chiral structure [18,22],
rose pirouette structure [23-25], conjugated gammadions structure [26],
and so on. All these structures can exhibit circular dichroism and
optical activity with negative index.

In this paper, we proposed a multi-band asymmetric CMM using a
double-layered Archimedean spirals array in which the bottom spirals
twist 90[degrees] compared to the upper spirals. In the unit cell, two
pairs of Archimedean spirals with different parameters are adopted to
construct the whole circular polarizer. The structure is novel due to
Archimedean spiral is intrinsic chirality, so the design is combined
intrinsic chirality with structure chirality. When a y-polarized EM wave
is incident on the proposed sample, it is found that relatively pure
circularly polarized wave can be obtained in transmission at four
resonance frequencies. S parameters retrieval results show that at three
resonant frequencies the effective refraction index is close to zero
[30], and the other is negative refraction index. The transformation
coefficient from a linearly polarized wave to a circularly polarized
wave is relatively high with respect to most of the negative refraction
index CMMs that have been reported [13, 21, 27]. The proposed multi-band
polarizer has simple geometry and is easily fabricated with conventional
printed circuit board technology, and can be used in applications such
as laser [31, 32], antenna [33-35], and remote sensors.

2. THEORETICAL ANALYSIS

Chiral metamaterials are made of unit cells without any mirror
symmetry so that the cross-coupling between electric and magnetic fields
exists at the resonance. Therefore, RCP wave and LCP wave would
encounter different transmission coefficients. The chiral medium can be
represented by the chirality parameter K Thus, the constitutive
relations in the CMMs are written as [10]

where [[epsilon].sub.0] and [[mu].sub.0] are the permittivity and
permeability of vacuum; [epsilon] and [mu] are the relative permittivity
and permeability of the CMMs. Electromagnetic field of chiral medium can
be stated as

The electric fields of RCP (+) wave and LCP (-) wave are defined as
[E.sub.[+ or -]]; [eta] = [square root of
[[mu].sub.0][mu]/[[epsilon].sub.0][epsilon] is wave impedance of CMMs.
According to Maxwell's equations and constitutive relations we can
get wave equation of [E.sub.[+ or -]]

([[nabla].sup.2] + [k.sup.2.sub.[+ or -]) [E.sub.[+ or -]] = 0 (3)

where [k.sub.[+ or -]] = [n.sub.[+ or -]][k.sub.0], [k.sub.0] =
[omega]/c is the free-space wave number vector; [n.sub.[+ or -]] are the
refractive indexes of RCP and LCP wave, which are given by:

[n.sub.[+ or -]] = n [+ or -] k (4)

where n = [square root of [epsilon][mu]]. From formula (4),
clearly, given a large enough chirality, the negativity of [n.sub.+] or
[n.sub.-] is possible, when n is approximately -[kappa], [n.sub.+]
approximates to zero, and when n is approximately [kappa], [n.sub.-]
approximates to zero. Based on this principle, we can design negative
refraction index or near-zero refraction index chiral metamaterials with
circular dichroism and optical activity, which can realize polarization
rotate of electromagnetic wave.

3. DESIGN, SIMULATION, AND EXPERIMENT

The unit cell of the CMM is depicted in Figure 1(a), which is
composed of two pairs of the Archimedean spirals, and the spirals in
diagonal are identical. The parameters of the spirals by No. 2 are
scaled down by a factor of 0.9 with respect to the parameters of the
spirals marked by No. 1. The spirals on the back side of the substrate
are twisted 90[degrees] with respect to the spirals on the front side.
The dielectric lamina is chosen to be Arlon AD 250 with relative
permittivity of 2.5 and loss tangent of 0.003. The thickness of the
lamina is t = 2.1 mm, and the copper pattern has a thickness of 0.03 mm.
The period constant of the CMM is represented by parameter a. The
following geometric parameters are used in the simulation and
experiment: a = 10 mm, r = 0.2 mm, w = 0.85 mm and g = 0.3 mm.

We started the analysis with numerical simulation of the CMM
structure using CST Microwave Studio which is based on the finite
difference time domain (FDTD) method. The boundaries are selected to be
periodic in the x and y directions and open the z direction. A
y-polarized wave propagating along +z direction is employed as the
excitation source. Due to the lack of C4 symmetric [36] in this CMM, the
response to the incident electric field along x direction is different
from y direction. In this work, y direction is chosen. In the
experiment, the chiral structure with a dimension of 15 x 15 unit cells
was fabricated, shown as Figure 1(b). A standard linearly polarized
double-ridge horn antenna is utilized as the transmitter while a planar
LCP antenna and a planar RCP antenna are employed as the receiver in
turn. The prototype is placed in the middle between the antennas. The
transmission coefficient measurements are performed using a vector
network analyzer of Agilent PNA E8362B. The transmission of circularly
polarized waves also can be converted from the linear transmission
coefficients co-polarization [T.sub.yy] and cross-polarization
[T.sub.xy], [T.sub.[+ or -]] = [T.sub.xy] [+ or -] i[T.sub.yy], where
the subscript "+" indicates the RCP wave, and the subscript
"-" indicates the LCP wave.

4. RESULTS AND DISCUSSION

Numerical and experimental circular transformation coefficients for
the RCP and LCP components are presented in Figures 2(a) and (b). There
are four obviously transmission peaks in the frequency band ranging from
13 GHz to 18 GHz. The simulated results reveal that the transmission of
the LCP wave reaches its minimum value at 14.28 GHz and 15.96 GHz, and
the transmission coefficients are -40.23 dB and -23.29dB, respectively.
The minimum contributions of the RCP component are observed at 15.3 GHz
as -29 dB, and at 16.88 GHz as -28 dB. It follows the feature of
circular polarizer that studied CMM originates from the different
circular polarization transformation coefficients for the RCP and LCP
components, due to a y-polarized incident wave. One of the circular
polarizations is eliminated at the resonance frequencies, whereas the
other polarization is transmitted with a small loss. As a result, at
14.28 GHz and 15.96 GHz, the transmitted wave is RCP. Similarly, at 15.3
GHz and 16.88 GHz, the LCP wave is transmitted.

The measured results are in good agreement with the simulated ones.
Due to the fabrication and measurement tolerance, the four measured
transmission gaps have slight shift with respect to simulation. We can
note that the transmission coefficients are both less than -30 dB at
these four resonances, and the measured transmission coefficients are
-3.3dB at 14.25 GHz, -0.54dB at 15.9 GHz, which are the resonances of
RCP wave; -1.78 dB at 15.27 GHz, and -2.5 dB at 16.9 GHz, which are the
resonances of LCP wave.

In order to understand the role that two pairs of spirals of array
play in the CMM, the transmission characteristics of the unit cell with
only the twisted spirals 1 (2) are calculated, and the results are
depicted in Figure 3. For the case of the only twisted spirals 1, the
bigger one, there are two obviously resonant frequencies in the range of
14-15.5 GHz, which are the LCP and RCP wave, respectively. For the case
of the only twisted spirals 2, the smaller one, it can be observed that,
the obvious difference between the transmission of LCP and RCP wave in
the frequency range 15.5-17 GHz. Based on the above results, it can draw
a conclusion that the bigger twisted spirals play an important role at
the lower frequencies, while the smaller ones are responsible for the
polarization rotation at the higher frequencies.

The ratio of the cross-polarization transmission and
co-polarization transmission [absolute value of [T.sub.xy]]/[absolute
value of [T.sub.yy]] and the phase difference [phi]([T.sub.xy])-
[phi]([T.sub.yy]) can also demonstrate the polarization characteristics
of the transmitted wave. Figure 4(a) shows the corresponding result. It
can be seen that the values of ratio [absolute value of
[T.sub.xy]]/[absolute value of [T.sub.yy]] and phase difference are 0.98
and 91.8[degrees] at 14.28 GHz, 1.06 and -91.7[degrees]
(268.3[degrees]-360[degrees]) at 15.3 GHz, 1.18 and 92.34[degrees] at
15.96 GHz, 0.92 and -88.27[degrees] at 16.88 GHz. The above results
indicate that the rotations of the transmitted field are right-handed at
14.28 GHz and 15.96 GHz, which are then changed to left-handed at 15.3
GHz and 16.88 GHz. In addition it can be found that the emitted fields
are close to the pure circularly polarized wave at these resonant
frequencies, which is in good agreement with the results of the circular
transmission in Figure 2.

In order to clearly demonstrate the optical activity of the
polarization rotator, polarization azimuth rotation angle [theta] and
ellipticity [eta] are calculated by the following formulas [37]

The polarization azimuth rotation angle [theta] denotes the
rotation angle between the polarization planes of the emitted and
incident waves, while the ellipticity [eta] represents the polarization
state of the emitted wave. When [eta] equals to zero, the emitted wave
is a linearly polarized wave that the polarization plane has a rotation
angle of [theta] relative to the incident wave, which indicates pure
optical activity is produced. The emitted wave would be circularly
polarized if [eta] equals to [+ or -] 45[degrees]. Figure 4(b) shows the
simulated results of the polarization azimuth rotation angle [theta] and
ellipticity [eta] of the transmitted wave. It can be clearly seen that,
the value of n is 44.1[degrees] at 14.28 GHz, -42.5[degrees] at 15.3
GHz, 40[degrees] at 15.96 GHz, -41.4[degrees] at 16.88 GHz. It means the
transmitted fields are close to pure circular polarization. In addition,
it also can be seen that the values of ellipticity [eta] are in the
vicinity of 0[degrees] at 14.5 GHz, 15.5 GHz and 16.5 GHz, the
polarization rotation angle [theta] are -27.6[degrees], 47.4[degrees]
and -38. 6[degrees], respectively, which corresponds a optical activity
effect. It indicates that the polarization plane of the emitted wave has
-27.6[degrees], 47.4[degrees] and -38. 6[degrees] rotation with respect
to the incident wave, respectively.

Figure 5 shows the retrieved effective parameters of the CMM based
on the simulated S parameters. In the Figure 5(a), the value of [kappa]
and n are: [n.sub.1] = 1.44, [[kappa].sub.1] = 1.35, [n.sub.2] = 1.26,
[[kappa].sub.2] = -1.23, [n.sub.3] = -1.14, [[kappa].sub.3] = 3.31,
[n.sub.4] = 0.64, [[kappa].sub.4] = -0.41, at the four resonant
frequencies in the order from the low frequency to the high frequency.
Using the formula (4), we calculate the refractive index of LCP wave
[n.sub.1] = [n.sub.1] - [[kappa].sub.1] = 0.09, [n.sub.3-] = [n.sub.3] -
[[kappa].sub.3] = -4.45, at the frequency 1 and frequency 3, the
refractive index of RCP wave [n.sub.2+] = [n.sub.2] + [[kappa].sub.2] =
0.03, [n.sub.4+] = [n.sub.4] + [[kappa].sub.4] = 0.23; at the frequency
2 and frequency 4, as shown in Figure 5(b). The results indicate that
for the LCP and RCP wave of the proposed CMM, the refraction index is
close to zero or negative due to strong chirality parameter K; and the
real parts of the retrieved effective permittivity [epsilon] and
permeability [mu] are presented in Figure 5(c).

The mechanism of resonances for the four Archimedes spirals CMM can
be understand by studying the surface current distributions on the upper
and bottom layer, as shown in Figure 6. For the first two resonant
frequencies of 14.28 GHz and 15.3 GHz, the strong surface current is
induced on the lager spirals, while relatively weak current energy
exists on the smaller ones, as denoted in Figures 6(a), (b), which means
the RCP and LCP wave caused by the lager spiral array in the whole
sample. Furthermore, the directions of the surface currents on the upper
and bottom layers are identical at 14.28 GHz, which exhibits some
characteristics similar to electric dipole and generates electric
resonance [38]; the directions of the surface currents on the upper and
bottom layers are opposite at 15.3 GHz, which exhibits some
characteristics similar to magnetic dipole and generates magnetic
resonance. The same analysis is also applicable to the second resonant
frequencies of the RCP and LCP wave, which the surface currents are
mainly distributed in the smaller spirals, as denoted in Figures 6(c),
(d). Due to the different forms of resonance in the CMM, the RCP wave
and LCP wave emerge different transmission coefficients, and then the
strong optical activity is obtained.

5. CONCLUSION

In conclusion, a multi-band CMM based on Archimedean spiral
structures is proposed. Both simulation and experiment results have
demonstrated that circular polarization wave is obtained at four
frequencies, when a y-polarized wave incidents on this sample. The
effective refractive index of RCP or LCP is close to zero or negative at
the vicinity of the resonances. The surface current distribution is
studied to understand that the larger twisted spirals array plays the
great role in the CMM at the lower frequency while the twisted spirals
array with smaller size is responsible for the higher polarization
rotation frequency. The design has multiple-frequency bands which can be
utilized as a circular polarizer for microwave applications and have
much potential application in the microwave domain.